Question 7
A,B,C,D,E are centres of five circles of radius 1 cm. $\angle ABC=90^\circ$, $\angle BAC=60^\circ$, $BC\parallel DE$. The circle pairs (A,D),(B,D),(D,E),(E,C) are externally tangent; all other pairs do not intersect. The maximum distance between two points chosen on the circles is $a+\sqrt b+\sqrt c$ cm, with positive integers $a,b,c$ and $b\lt c$. Find $a+10b+100c$.
